x=a+b+4 and a is inversely proportional to y²; b is inverseley propotional to 1/y. when y = 2 x = 18 and when y = 1 x = -3. find x when y = 4​

Answer:

When y = 4, x is equal to 39

Step-by-step explanation:

The given parameters are;

x = a + b + 4

a ∝ 1/y²

b ∝ 1/(1/y) = y

When y = 2, x = 18

When y = 1, x = -3

Therefore, we have;

a·y² = j

a = j/y²

b ∝ 1/(1/y)

∴ b ∝ y

b = k·y

When y = 2, x = 18, we have;

a = j/y² = j/2² = j/4

b = k·y = k·2

x = a + b + 4

∴ 18 = j/4 + k·2 + 4...(1)

When y = 1, x = -3, we have;

a = j/y² = j/1² = j

b = k·y = k·1 = k

x = a + b + 4

∴ -3 = j + k + 4...(2)

Making 'j', the subject of equation (1) and (2) gives;

From equation (1), we have;

18 = j/4 + k·2 + 4

∴ j = (18 - 4 - k·2) × 4 = 56 - 8·k

From equation (2), we have;

-3 = j + k + 4

∴ j = -3 - 4 - k = -7 - k

Equating the two values of 'j', gives;

56 - 8·k = -7 - k

56 + 7 = 8·k - k

63 = 7·k

k = 63/7 = 9

k = 9

From equation (2), we get;

-3 = j + k + 4

k = 9

∴ -3 = j + 9 + 4

j = -3 - 9 - 4 = -16

j = -16

When y = 4, we get;

x = a + b + 4

a = j/y²

b = k·y

∴ x = j/y² + k·y + 4

Plugging in the values of 'j', and 'k' and y = 4, gives;

x = (-16)/y² + 9·y + 4

∴ x = (-16)/4² + 9 × 4 + 4 = 39

x = 39

Therefore;

When y = 4, x = 39.

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​

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